Quest for Unification

Here I have explicitly displayed the pairs (ν, e−) and (u, d) as weak doublets, but I have not explicitly shown the color quantum numbers of u, d and u, d. The subscript is the hypercharge quantum number Y . This structure looks strange at first sight. Part of the strangeness, relative to the way physics was formerly understood, is that the leftand right-handed fermions transform differently under the standard model gauge symmetries. With time, physicists came to see this as a virtue: it means that the quarks and leptons cannot have bare masses and can only gain mass from the Higgs mechanism. So it explains why they cannot be much heavier than the W and Z bosons (which gain mass from the same Higgs mechanism) and in particular why they are light compared to hypothetical fundamental scales in physics such as the Planck scale of gravity. But there is another side to the strangeness in the structure of the standard model. A single generation of quarks and leptons is made by putting together quite a few odd bits and pieces, with strange fractions, in particular, for the hypercharge quantum numbers. Anomaly cancellation depends on obscure calculations like Tr Y 3 = 2(−1)3 + 6(1/3) + 3(−4/3)3 + 3(2/3) + 2 = 0. (2)